Question

Pfd Company has debt with a yield to maturity of 5.7%​, a cost of equity of 13.5%​, and a cost of preferred stock of 8.7%. The market values of its​ debt, preferred​ stock, and equity are $10.2 ​million, $2.6 ​million, and $15.2 ​million, respectively, and its tax rate is 40%. What is this​ firm's after-tax​ WACC?

Answer 1

According to the given information,
Pre-tax Cost of debt = 5.7%
Cost of equity = 13.5%
Cost of preferred stock = 8.7%

Value of debt = $10.2 million
Value of preferred stock = $2.6 million
Value of equity = $15.2 million

Total value = Value of debt + Value of preferred stock + Value of equity
                 = $10.2 + $2.6 + $15.2
                 = $28 million

Weight of debt = Value of debt / Total value

                       = $10.2 / $28

                      = 36.43%

Weight of preferred stock = Value of preferred stock / Total value

                                       = $2.6 / $28

                                       = 9.29%

Weight of equity = Value of equity / Total value

                         = $15.2 / $28

                        = 54.29%

First, we have to compute the after-tax cost of debt

After-tax cost of debt = pre-tax cost of debt (1-tax rate)

                                = 0.057 (1 - 0.40)

                                = 3.42%

Therefore, the value of after-tax cost of debt is 3.42%

The formula for calculating the WACC is

WACC = [Wd * Rd] + [Wp * Rp] + [We * Re]

where Wd is the weight of debt

          Rd is the after-tax cost of debt

         Wp is the weight of preferred stock

         Rp is the cost of preferred stock

        We is the weight of equity

        Re is the cost of equity

Substituting the values in the above formula, we get

WACC = [0.364 * 0.0342] + [0.093 * 0.087] + [0.543 * 0.135]

         = 0.0125 + 0.0081 + 0.0733

         = 0.0938 or 9.38%

Therefore, the value of WACC is 9.38%